Stochastic Dynamics in Near-Critical Supercritical Fluids

Temperature-driven irreversible generalized Langevin equation can capture the nonequilibrium dynamics of two dissipated coupled oscillators

Kawai and Komatsuzaki [J. Chem. Phys. 134, 114523 (2011)] recently derived the nonequilibrium generalized Langevin equation (GLE) for a nonstationary system using the projection operator technique. In the limit when the environment is slowly changing (that is, a quasi-equilibrium bath), it should reduce to the irreversible GLE approach (iGLE) [J. Chem. Phys. 111, 7701 (1999)]. Kawai and Komatsuzaki, however, found that the driven harmonic oscillator, an example of a nonequilibrium system does not obey the iGLE presumably because it did not quite satisfy the limiting conditions of the latter. Notwithstanding the lack of a massive quasi-equilibrium bath (one of the conditions under which the iGLE had been derived earlier), we found that the temperature-driven iGLE (T-iGLE) [J. Chem. Phys. 126, 244506 (2007)] can reproduce the nonequilibrium dynamics of a driven dissipated pair of harmonic oscillators. It requires a choice of the function representing the coupling between the oscillator coordinate and the bath and shows that the T-iGLE representation is consistent with the projection operator formalism if only dominant bath modes are taken into account. Moreover, we also show that the more readily applicable phenomenological iGLE model is recoverable from the Kawai and Komatsuzaki model beyond the adiabatic limit used in the original T-iGLE theory.

Phase induced current in presence of nonequilibrium bath: A quantum approach

Based on a system-reservoir nonlinear coupling model, where the associated bath is externally driven by a fluctuating force, we present a microscopic approach to quantum state-dependent diffusion and multiplicative noises in terms of a quantum (Markovian) Langevin equation in overdamped limit when the associated bath is in nonequilibrium state. We then explore the possibility of observing a quantum current when the bath is modulated by white noise, the phenomena which is absent in the classical regime.

Multiplicative cross-correlated noise induced escape rate from a metastable state

We present an analytical framework to study the escape rate from a metastable state under the influence of two external multiplicative cross-correlated noise processes. By starting from a phenomenological stationary Langevin description with multiplicative noise processes, we have investigated the Kramers theory for activated rate processes in a nonequilibrium open system (one dimensional in nature) driven by two external cross-correlated noise processes which are Gaussian, stationary, and delta correlated. Based on the Fokker-Planck description in phase space, we then derive the escape rate from a metastable state in the moderate to large friction limit to study the effect of degree of correlation on the same. By employing numerical simulation in the presence of external cross-correlated additive and multiplicative noises, we check the validity of our analytical formalism for constant dissipation, which shows a satisfactory agreement between both the approaches for the specific choice of noise processes. It is evident both from analytical development and the corresponding numerical simulation that the enhancement of rate is possible by increasing the degree of correlation of the external fluctuations.

Dynamics of a metastable state nonlinearly coupled to a heat bath driven by external noise

Based on a system-reservoir model, where the system is nonlinearly coupled to a heat bath and the heat bath is modulated by an external stationary Gaussian noise, we derive the generalized Langevin equation with space-dependent friction and multiplicative noise and construct the corresponding Fokker-Planck equation, valid for short correlation time, with space-dependent diffusion coefficient to study the escape rate from a metastable state in the moderate- to large-damping regime. By considering the dynamics in a model cubic potential we analyze the results numerically which are in good agreement with theoretical predictions. It has been shown numerically that enhancement of the rate is possible by properly tuning the correlation time of the external noise.

Static and dynamic critical behavior of a symmetrical binary fluid: A computer simulation

A symmetrical binary, A+B Lennard-Jones mixture is studied by a combination of semi-grand-canonical Monte Carlo (SGMC) and molecular dynamics (MD) methods near a liquid-liquid critical temperature T(c). Choosing equal chemical potentials for the two species, the SGMC switches identities (A-->B-->A) to generate well-equilibrated configurations of the system on the coexistence curve for T<T(c) and at the critical concentration, x(c)=12, for T>T(c). A finite-size scaling analysis of the concentration susceptibility above T(c) and of the order parameter below T(c) is performed, varying the number of particles from N=400 to 12 800. The data are fully compatible with the expected critical exponents of the three-dimensional Ising universality class. The equilibrium configurations from the SGMC runs are used as initial states for microcanonical MD runs, from which transport coefficients are extracted. Self-diffusion coefficients are obtained from the Einstein relation, while the interdiffusion coefficient and the shear viscosity are estimated from Green-Kubo expressions. As expected, the self-diffusion constant does not display a detectable critical anomaly. With appropriate finite-size scaling analysis, we show that the simulation data for the shear viscosity and the mutual diffusion constant are quite consistent both with the theoretically predicted behavior, including the critical exponents and amplitudes, and with the most accurate experimental evidence.

Escape rate from a metastable state weakly interacting with a heat bath driven by external noise

Based on a system-reservoir model, where the reservoir is driven by an external stationary, Gaussian noise with arbitrary decaying correlation function, we study the escape rate from a metastable state in the energy diffusion regime. For the open system we derive the Fokker-Planck equation in the energy space and subsequently calculate the generalized non-Markovian escape rate from a metastable well in the energy diffusion domain. By considering the dynamics in a model cubic potential we show that the results obtained from numerical simulation are in good agreement with the theoretical prediction. It has been also shown numerically that the well-known turnover feature can be restored from our model.

Dynamics of Swelling/Contracting Hard Spheres Surmised by an Irreversible Langevin Equation

The diffusion of molecules through uniform homogeneous materials can readily be described by Brownian motion or generalizations thereof. The further generalization of these models to describe molecular diffusion through heterogeneous and nonstationary solvents is much less understood. Phenomenological nonstationary generalizations of the generalized Langevin equation (GLE) have earlier been developed satisfying the fluctuation-dissipation relationship in quasi-equilibrium limits while exhibiting somewhat complex behavior away from equilibrium. This reduced-dimensional representation should be capable of describing the diffusion of a particle through a colloidal suspension whose average particle size is tuned by an external driving force such as pH. A simple particle model of such a process involves the motion of a hard-sphere particle in an explicit environment of swelling hard spheres. The velocity autocorrelation functions observed in a large number of simulations of the particle model under various swelling rates agree precisely with those of a single form of the nonstationary phenomenological model. Though this procedure is not an explicit projection of the mechanical system onto the nonstationary GLE, it does show that the latter correctly describes the dynamics of the projected coordinate--namely, diffusion of the solute--under nonequilibrium conditions. Both nonequilibrium solvent models lead to behavior reminiscent of beta-relaxation processes at packing fractions substantially below that of the glass transition.

An idealized model for nonequilibrium dynamics in molecular systems

The nonequilibrium dynamics of highly nonlinear and multidimensional systems can give rise to emergent chemical behavior which can often be tracked using low-dimensional order parameters such as a reaction path. Such behavior cannot be readily surmised by stationary projected stochastic representations such as those described by the Langevin equation or the generalized Langevin equation (GLE). The irreversible generalized Langevin equation (iGLE) contains a nonstationary friction kernel that in certain limits reduces to the GLE with space-dependent friction. For more general forms of the friction kernel, the iGLE was previously shown to be the projection of a mechanical system with a time-dependent Hamiltonian [R. Hernandez, J. Chem. Phys. 110, 7701 (1999)]. In the present work, the corresponding open Hamiltonian system is shown to be amenable to numerical integration despite the presence of a nonlocal term. Simulations of this mechanical system further confirm that the time dependence of the observed total energy and the correlations of the solvent force are in precise agreement with the projected iGLE. This extended nonstationary Hamiltonian is thus amenable to the study of nonequilibrium bounds and fluctuation theorems.

Dynamics of fluids near the consolute critical point: A molecular-dynamics study of the Widom–Rowlinson mixture

Molecular-dynamics simulations are presented for the dynamic behavior of the Widom-Rowlinson mixture [B. Widom, and J. S. Rowlinson, J. Chem. Phys. 52, 1670 (1970)] at its critical point. This model consists of two components where like species do not interact and unlike species interact via a hard-core potential. Critical exponents are obtained from a finite-size scaling analysis. The self-diffusion coefficient shows no anomalous behavior near the critical point. The shear viscosity and thermal conductivity show no divergent behavior for the system sizes considered, although there is a significant critical enhancement. The mutual diffusion coefficient, D(AB), vanishes as D(AB) approximately xi(-1.26 +/- 0.08), where xi is the correlation length. This is different from the renormalization-group (D(AB) approximately xi(-1.065)) mode coupling theory (D(AB) approximately xi(-1)) predictions. The theories and simulations can be reconciled if we assume that logarithmic corrections to scaling are important.

Chemical reaction dynamics within anisotropic solvents in time-dependent fields

The dynamics of low-dimensional Brownian particles coupled to time-dependent driven anisotropic heavy particles (mesogens) in a uniform bath (solvent) have been described through the use of a variant of the stochastic Langevin equation. The rotational motion of the mesogens is assumed to follow the motion of an external driving field in the linear response limit. Reaction dynamics have also been probed using a two-state model for the Brownian particles. Analytical expressions for diffusion and reaction rates have been developed and are found to be in good agreement with numerical calculations. When the external field driving the mesogens is held at constant rotational frequency, the model for reaction dynamics predicts that the applied field frequency can be used to control the product composition.

Separation of biosynthetic polyunsaturated fatty acid (PUFA) with supercritical fluid

The separation of biosynthetic polyunsaturated fatty acid (PUFA) was undertaken with supercritical fluid. The polyunsaturated fatty acid was synthesised by WL-1021, which is a strain of marine bacterium isolated from marine fish. The polyunsaturated fatty acid can be very efficiently extracted from WL-1021 that has the characteristics of rapid growth in the artificial medium. The PUFA in WL-1021 has been successfully separated by supercritical fluid extraction (SFE). The SFE process parameters including pressure, temperature and culture temperature variations have been measured by High Performance Liquid Chromatography (HPLC), GC/FT-IR and GC/MS.